Square Root of 777
2026-02-28 08:24 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-777

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

Step 1: To begin with, we need to group the numbers from right to left. In the case of 777, we need to group it as 77 and 7.

Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 x 2 is less than or equal to 7. Now the quotient is 2; after subtracting 4 from 7, the remainder is 3.

Step 3: Now let us bring down 77, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 40 (as 4 becomes 40 by adding a digit). We need to find the value of n such that 40n x n ≤ 377.

Step 5: Let's try n = 9. Now 409 x 9 = 3681.

Step 6: Subtract 3681 from 3770, the difference is 89, and the quotient is 27.9.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 8900.

Step 8: Now we need to find the new divisor, which is 558 because 558 x 8 = 4464.

Step 9: Subtracting 4464 from 8900, we get the result 4436.

Step 10: Now the quotient is 27.87.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √777 is approximately 27.8747.